Strapdown Inertial Navigation System Algorithms Based on Geometric Algebra

Wu, Dimin; Wang, Zhengzhi

doi:10.1007/s00006-012-0326-8

Cited by 13 publications

(9 citation statements)

References 17 publications

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“…As long as ω is known as a function of time and possibly of R (but not of dR/dt), standard theorems on ordinary differential equations apply, which show that given initial data for R, we can simply evolve the four components of this equation to find R as a function of time. 5 We will see below that quaternions can be exponentiated readily. One might then expect that Eq.…”

Section: Integration Of Rotorsmentioning

confidence: 99%

“…Though the principle may be the same, the noise and discrete nature of the angular velocity suggest that low-order methods would be preferable for these devices. This, of course, is a particular example in the broader field of strapdown inertial navigation systems [2][3][4][5]. In a completely different setting, Simo [6] pointed out that uniform beams undergoing twisting and bending obey equations formally identical to those for angular velocity, where time is replaced by arc length along the beam and the angular velocity is replaced by the rate of twisting per unit length.…”

Section: Introductionmentioning

confidence: 99%

“…This particular problem has even been analyzed using the methods of geometric algebra. Such problems have been analyzed previously in the literature [2][3][4][5][7][8][9][10], but those approaches are designed very specifically for pure rotational (and possibly translational) problems without any other evolved quantities, and are frequently tailored even further to approximate particular subclasses of motion. They are therefore not suitable when high accuracy is needed for long integrations involving complicated rotations and other coupled quantities evolving with multiple timescales.…”

Section: Introductionmentioning

confidence: 99%

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The Integration of Angular Velocity

Boyle

2017

Adv. Appl. Clifford Algebras

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A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential equations. Several possible approaches are examined, along with various improvements over previous efforts. These are then evaluated numerically by comparison to a complicated but analytically known rotation that is motivated by the important astrophysical problem of precessing black-hole binaries. It is shown that a straightforward solution directly using quaternions is most efficient and accurate, and that the norm of the quaternion is irrelevant. Integration of the generator of the rotation can also be made roughly as efficient as integration of the rotation. Both methods will typically be twice as efficient naive vector-or matrix-based methods. Implementation by means of standard general-purpose numerical integrators is stable and efficient, so that such problems can be readily solved as part of a larger system of differential equations. Possible generalization to integration in other Lie groups is also discussed.

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Section: Integration Of Rotorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Integration of Angular Velocity

Boyle

2017

Adv. Appl. Clifford Algebras

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“…Chelnokov [ 13 ] proved that the DQ solutions were stable in Lyapunov’s sense and the two-speed DQ algorithm achieved the third and fourth order of accuracy. In [ 14 , 15 ], geometry algebra and Lie group methods were used to construct the two-speed velocity update algorithms with comparable accuracy to the DQ algorithm. In addition, a simplified parallel velocity error compensation algorithm was proposed in [ 16 , 17 ] based on the two-speed velocity update concept and executed on a single-chip field programmable gate array (FPGA).…”

Section: Introductionmentioning

confidence: 99%

Sculling Compensation Algorithm for SINS Based on Two-Time Scale Perturbation Model of Inertial Measurements

Wang

Xin

2018

Sensors

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In order to decrease the velocity sculling error under vibration environments, a new sculling error compensation algorithm for strapdown inertial navigation system (SINS) using angular rate and specific force measurements as inputs is proposed in this paper. First, the sculling error formula in incremental velocity update is analytically derived in terms of the angular rate and specific force. Next, two-time scale perturbation models of the angular rate and specific force are constructed. The new sculling correction term is derived and a gravitational search optimization method is used to determine the parameters in the two-time scale perturbation models. Finally, the performance of the proposed algorithm is evaluated in a stochastic real sculling environment, which is different from the conventional algorithms simulated in a pure sculling circumstance. A series of test results demonstrate that the new sculling compensation algorithm can achieve balanced real/pseudo sculling correction performance during velocity update with the advantage of less computation load compared with conventional algorithms.

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“…To overcome the limitation, Wu et al (2005) developed the Dual Quaternion (DQ) algorithm which combined rotation and translation as a whole. The geometry algebra INS algorithm (Wu and Wang, 2012) is similar to the DQ algorithm. Later, Savage (2006b) proposed the Velocity Translation Vector (VTV) and Position Translation Vector (PTV) which achieved exact solutions to rigid body translation.…”

Section: Introductionmentioning

confidence: 99%

Strapdown Inertial Navigation Algorithms Based on Lie Group

Mao

Lian

2016

J. Navigation

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This paper presents a framework for a strapdown Inertial Navigation System (INS) algorithm design by using Lie group and Lie algebra. The general way to solve Lie group differential equations is introduced. Investigations reveal that this general Lie group method provides a simpler unified way to solve differential equations involving direction cosine matrix, quaternion and dual quaternion, which are widely used in INS algorithm design. Furthermore, we also present a new INS algorithm based on the Special Euclidean group se(3) under the guidelines of Lie group method. Analyses show that se(3) algorithm has the same accuracy as a dual quaternion algorithm, this is also justified by numerical simulations. Though the se(3) algorithm has no improvements in accuracy, the general Lie group method used in the design process shows its brevity and uniformity.

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Strapdown Inertial Navigation System Algorithms Based on Geometric Algebra

Cited by 13 publications

References 17 publications

The Integration of Angular Velocity

The Integration of Angular Velocity

Sculling Compensation Algorithm for SINS Based on Two-Time Scale Perturbation Model of Inertial Measurements

Strapdown Inertial Navigation Algorithms Based on Lie Group

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